Mistakes give rise to problems- 2

We know that we can split a fraction like what we did above, but you can't do this in

\[\dfrac{a}{b+c} = \dfrac{a}{b} + \dfrac{a}{c} \]

This is a false property, it will be a mistake if you do it! However, it holds for certain values of integers \(a,b,\) and \(c.\) If \(a,b,c \leq 10\) and \(a,b,c\) are non-negative integers, then for how many ordered triples \((a,b,c)\) is \( \frac a{b+c} = \frac ab + \frac ac \) seen to be true?